Crimson Sea

When you get to the research center on Crimson (the big red place with a lot of "Mutons"). Buy a lot of parts for your weapon and finish the level with them. The next time you return to quest mode you should get the weapon parts you bought in the last mission. You can sell those and get new ones. You can still keep the old weapons if you finished the level with them. The same works for your Neo-Psionics.

Have at least 2 Medixir items, the Leviathan 3, and Vulcan 3 barrels. Use L so you can sway from left to right, keeping the monster in your screen. Take the Boss' HP all the way down until he has only a little remaining. Use the Leviathan 3 to do this, then use the Vulcan 3 for the finishing touch. You will probably have to use at least one Medixir before this point. Make sure you do not use the other. Wait until you die to use it. Do not use any Neo-Psionics to fight him; only use Cure 2 and 3 on yourself.